Quick Explode Modifier in Blender Internal Does Not Affect All Objects
With quick explode, under the modifier settings ensure that dead is not ticked on.


Otherwise, the particles will not disappear after their lifetime. Under default settings, this is the only reason that I know of that the particles should remain. If your animation is shorter than 50 frames however, which is the default, then go to the particle tab and change the lifetime of the objects particle system as needed.